The embodiments described herein relate generally to finite element analysis and, more particularly, to finite element analysis (FEA) simulation of structures having a large number of degrees of freedom.
Substructuring techniques (or Component Mode Synthesis) are commonly employed in the finite element framework for analyzing large, complex structural systems. These techniques make local design modifications easier and accelerate model assembly process. Especially in the design stage of large vehicle models, substructuring techniques are frequently used to reduce the size of assembled systems and, consequently, the cost of subsequent analyses with the assembled system. To reduce the size of a large system using substructuring techniques, truncated normal modes are commonly used in addition to the constraint (sometimes also referred to as static) modes. To satisfy the increased accuracy requirement for the finite element models at higher frequencies, the model system size grows significantly and many substructure eigenmodes are required.
One known method of solving large-scale eigenvalue problems is the automated multilevel substructuring (AMLS) technique. The AMLS technique is also used to speed up the eigensolution process for large substructure generation. However, generating substructures, which includes projecting the substructure system matrices on to the substructure modal space that includes eigenmodes and constraint modes, takes significant computational time and requires a huge amount of computer resources because the full substructure modes for a large substructure need to be stored for recovery later and retrieved for the condensed matrix computation in the substructure generation process. Within a conventional dynamic substructure generation procedure for large-scale models, computing eigenmodes is mandatory and the costs of computing constraint modes and projecting system matrices (i.e., stiffness, mass, damping matrices, and force vectors) onto substructure modal space are very high because the projection is performed using full substructure modes in the physical space, the size of which can easily be more than tens of millions degrees of freedom.